Santa Cruz took his tally to three goals in seven matches with a fifth-minute header at a corner followed by a penalty 10 minutes later after Brazilian midfielder Alemao was brought down by Ivan Estrada at the Estadio Azul.
Cruz Azul have 22 points from 13 matches, one point behind leaders Veracruz and Tijuana in the Clausura championship table.
Veracruz's 1-1 draw at home to bottom side Morelia on Friday lifted them into first place above Tijuana, beaten 2-1 at Queretaro, on goal difference.
"Obviously, I would have liked to score many more goals and have a greater influence in the team's game," Santa Cruz, who missed five matches through injury and scored his first goal for Cruz Azul against Tijuana three weeks ago, had said in midweek.
"Always a forward who arrives (at a new club) carries a weight (of expectation) and a greater responsibility," added the 33-year-old former Bayern Munich, Manchester City and Malaga striker, who joined Cruz Azul in January.
Title holders America could have gone top with a win at Monterrey but they were held 1-1 and are in third place with 22 points above Cruz Azul on goal difference.
Striker Dorlan Pabon put Monterrey ahead in the 16th minute with a low shot from the edge of the box and centre back Pablo Aguilar equalised for the champions with a header in the 20th.
Guadalajara, who have 21 points, can go top on Sunday if they beat Leon at the Omnilife.
(Reporting by Carlos Calvo; Writing by Rex Gowar in Buenos Aires; Editing by Greg Stutchbury)
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